Defect‑Driven Magnetism and Strain Engineering in Monolayer WSe2: A DFT Study

Introduction

Monolayer transition‑metal dichalcogenides (TMDs) such as WSe₂ possess a direct band gap (~1.6 eV) and high carrier mobility (~250 cm²/Vs), making them attractive for next‑generation electronics and optoelectronics. However, pristine WSe₂ is intrinsically non‑magnetic, limiting its use in spin‑based devices. Defects—particularly vacancies—are ubiquitous in 2D materials and can profoundly modify their electronic structure and magnetic behavior. Previous studies have shown that vacancies in graphene, MoS₂, and BaTiO₃ can induce magnetism. Strain engineering is another powerful tool; monolayer WSe₂ can withstand >10 % strain, enabling band‑gap and magnetic modulation. Here, we systematically explore the combined effects of vacancy defects and biaxial tensile strain on monolayer WSe₂ using state‑of‑the‑art DFT calculations.

Computational Methods

All calculations were performed with the Vienna Ab‑initio Simulation Package (VASP) using the PBE functional and PAW pseudopotentials. A plane‑wave cutoff of 300 eV and a 3×3×1 k‑point mesh were employed for a 5×5×1 supercell. Structures were relaxed until forces dropped below 0.02 eV/Å, and total‑energy convergence was set to 10⁻⁴ eV. Biaxial tensile strain (ε) was defined as ε = (c − c₀)/c₀ × 100 %. Formation energies were calculated via E_form = E_defect − E_pristine + ∑n_iu_i, where u_i are atomic chemical potentials.

Results and Discussion

Pristine Monolayer WSe₂

The relaxed 1H‑WSe₂ structure shows W–W and W–Se bond lengths of 3.31 Å and 2.54 Å, in agreement with experiment. The PBE band gap is 1.54 eV; HSE06 yields a more accurate 2.0 eV gap, confirming its direct‑gap semiconductor nature.

a Top and side views of monolayer WSe₂. b Band structure and DOS; Fermi level at 0 eV.

Vacancy‑Induced Electronic and Magnetic States

We examined seven vacancy configurations: single‑atom (V_Se, V_W), double‑atom (V_Se‑Se, V_Se2, V_W2), and larger complexes (V_WSe3, V_WSe6). Formation energies show that single‑Se vacancies are the most likely to form, while larger defects require higher energy inputs.

Electronic structure analysis reveals that V_Se, V_Se‑Se, V_W, and V_WSe3 remain non‑magnetic semiconductors but with reduced gaps (1.18 eV, 1.15 eV, 0.18 eV, 0.76 eV, respectively). In contrast, V_W2 becomes half‑metallic, exhibiting a 0.19 eV minority‑spin gap and a net moment of 2 μ_B. V_WSe6 shows a magnetic semiconductor behavior with a 6 μ_B moment and a narrow gap.

Band structures for V_Se–V_WSe6 vacancies. Blue/red lines: majority/minority spins; Fermi level at 0 eV.

Partial density‑of‑states (PDOS) analyses attribute the impurity states to W d and Se p orbitals near the vacancies. For V_W2, Se p_x dominates the conduction edge, while W d_{x²–y² and dz² shape the valence edge.}

PDOS for each vacancy type; NN_W and NN_Se denote nearest neighbors.

Effect of Biaxial Tensile Strain

Applying 0–7 % biaxial strain to pristine WSe₂ does not induce magnetism and reduces the band gap to 0.5 eV at 7 % strain. For defected systems, strain systematically narrows the gaps of V_Se, V_Se‑Se, and V_WSe3 from ~1.1 eV to 0.5 eV, 0.5 eV, and 0.3 eV, respectively. V_W, V_W2, and V_WSe6 remain <0.2 eV gaps under strain.

Crucially, tensile strain transforms the non‑magnetic V_W defect into a magnetic state with a 4 μ_B moment beyond 1 % strain, while V_W2 and V_WSe6 maintain their magnetic moments (6 μ_B up to 6 % strain, decreasing to 4 μ_B at 7 %). Spin‑density plots confirm that magnetism originates from W and adjacent Se atoms.

Band structures under 1 %, 4 %, and 7 % strain for all vacancy types.

a Energy gaps vs. strain for V_Se, V_Se‑Se, V_WSe3. b Magnetic moments vs. strain for V_W, V_W2, V_WSe6.

Spin‑resolved charge density for V_W, V_W2, V_WSe6 under 0–7 % strain; yellow = positive, cyan = negative spin density.

Conclusion

Our DFT study demonstrates that vacancy engineering, combined with biaxial tensile strain, can transform monolayer WSe₂ from a non‑magnetic semiconductor into a magnetic half‑metal or magnetic semiconductor. Single‑Se and W vacancies reduce the band gap but retain non‑magnetism; double‑W vacancies and the V_WSe6 complex introduce sizable magnetic moments (2 μ_B and 6 μ_B, respectively). Tensile strain further tunes both electronic gaps and magnetic moments, offering a practical route to design 2D magnetic semiconductors for spin‑tronics and valleytronics applications.